Translational Diffusion and Self-Association of an Intrinsically Disordered Protein κ-Casein Using NMR with Ultra-High Pulsed-Field Gradient and Time-Resolved FRET

Much attention has been given to studying the translational diffusion of globular proteins, whereas the translational diffusion of intrinsically disordered proteins (IDPs) is less studied. In this study, we investigate the translational diffusion and how it is affected by the self-association of an IDP, κ-casein, using pulsed-field gradient nuclear magnetic resonance and time-resolved Förster resonance energy transfer. Using the analysis of the shape of diffusion attenuation and the concentration dependence of κ-casein diffusion coefficients and intermolecular interactions, we demonstrate that κ-casein exhibits continuous self-association. When the volume fraction of κ-casein is below 0.08, we observe that κ-casein self-association results in a macroscopic phase separation upon storage at 4 °C. At κ-casein volume fractions above 0.08, self-association leads to the formation of labile gel-like networks without subsequent macroscopic phase separation. Unlike α-casein, which shows a strong concentration dependence and extensive gel-like network formation, only one-third of κ-casein molecules participate in the gel network at a time, resulting in a more dynamic and less extensive structure. These findings highlight the unique association properties of κ-casein, contributing to a better understanding of its behavior under various conditions and its potential role in casein micelle formation.


CIRCULAR DICHROISM (CD) SPECTROSCOPY OF κ-CASEIN
. For the far UV CD spectroscopic measurements, the lyophilized powder of κ-casein was dissolved in H 2 O at the concentrations of 0.001 to 0.006% (0.01 to 0.06 mg/mL).CD measurements were performed using a Jasco-1500 spectropolarimeter, equipped with a Peltier temperature control system.CD spectra were recorded using a 50 nm/min scan rate, a 4 s D.I.T. response, and a 1 nm bandwidth.Spectra were recorded in the range of 185-260 nm using a quartz glass cell with a path length, l, of 1 mm.The corresponding buffer baseline was subtracted from the spectra.Reported spectra are averages of 3-5 scans and are expressed as mean-residue molar ellipticity, [θ], calculated according to the following formula: where M 0 is the mean residue molar mass, θ λ is the measured ellipticity in degrees, and C is the protein concentration.CD spectra demonstrate that κ-casein does not have significant secondary structure at our experimental conditions.    2 , where g is the magnitude of pulsedfield gradient, A(0) is the spin-echo amplitude at g = 0, γ is the gyromagnetic ratio for protons, δ is the gradient pulse duration and t d = Δ -δ/3 is the diffusion time.

THE FÖRSTER DISTANCE CALCULATION
The Förster distance, R 0 = 2.6 nm, was calculated according to the formula 3 : ( ) where λ is the wavelength, J(λ) is the spectral overlap integral between the normalized donor emission spectrum F D (λ) and the acceptor absorption spectrum ε A (λ), k 2 = 2/3 is the probes orientation factor, η =1.4 is the refraction index of the medium, and Q D is the quantum yield of donor-only labeled protein (Q D = 0.11).Q D was estimated by the comparison to the quantum yield of quinine sulfate in 0.05 M H 2 SO 4 at λ ex = 347.5 nm (Q S =0.51 4 ), according to the equation: where F(λ) is the integral emission and A(λ) is the absorbance at the excitation wavelength of donor-labeled protein or quinine sulfate.The analysis of time-resolved fluorescence data was performed using the software package FargoFit, designed by I.V. Negrashov, executing the global least-square fitting of multiple time-resolved luminescence waveforms using different models with ability to link fitting parameters between waveforms.

Figure S7.
The linear dimensions of a κ-casein molecule were obtained using PSIPRED workbench 5 , a secondary structure prediction method that incorporates two feedforward neural networks which perform an analysis on output obtained from PSIBLAST (Position Specific Iterated -BLAST).

Figure S1 .
Figure S1.Amino acid sequence alignment with residues properties highlighted according to CLUSTAL color scheme: red -charged, blue -aromatic, green -aliphatic, orange -S, T, A, G, P.

Figure S2 .
Figure S2.Denaturing SDS-PAGE analysis shows that kcasein is a pure monodisperse species.

Figure S5 .
Figure S5.Spectra of diffusion coefficients of κ-casein (red, non-exponential diffusion attenuation) and water (blue, exponential diffusion attenuation) for an aqueous solution of κ-casein at a protein concentration of 0.1% as a function of the numbers of iterations N i .

Figure S6 .
Figure S6.Diffusion attenuations recorded in κ-casein solution with protein concentration of 5%.Curve 1 corresponds to the 5 % κ-casein sample obtained by dissolving a 20 % κ-casein solution.Curve 2 corresponds to the 5 % κ-casein sample prepared directly at this concentration.k = (γδg)2 , where g is the magnitude of pulsedfield gradient, A(0) is the spin-echo amplitude at g = 0, γ is the gyromagnetic ratio for protons, δ is the gradient pulse duration and t d = Δ -δ/3 is the diffusion time.